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Let S be a closed Shimura variety uniformized by the complex n-ball. The Hodge conjecture predicts that every Hodge class in H2k(S, Q), k = 0, . . . , n, is algebraic. We show that this holds for all ...
Matroids and quotients of spheres     Matroids  quotients  spheres       2015/8/25
For any linear quotient of a sphere, X = Sn−1/Γ, where Γ is an elementary abelian p–group, there is a corresponding Fp representable matroid MX which only depends on the isometry class of X. Whe...
An Application of Harnack Inequalitise to Random Walk on Nilpotent Quotients
First, we study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of a free group acts. Then using it, we define a descendin...
Abstract: Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-ar...
Abstract: The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order,...
Abstract: In this article we study left I-orders in the bicyclic monoid $\mathcal{B}$. We give necessary and sufficient conditions for a subsemigroup of $\mathcal{B}$ to be a left I-oreder in $\mathca...
Abstract: R. Canfield has conjectured that for all subgroups G of the automorphism group of the Boolean lattice B(n) (which can be regarded as the symmetric group S(n)) the quotient order B(n)/G is a ...
Let p and q be two distinct prime numbers, and Xpq/wq be the quotient of the Shimura curve of discriminant pq by the Atkin-Lehner involution wq. We describe a way to verify in wide generality a criter...
We compute presentations for the finite quotients $\mathcal{G}_n=\mathcal{G}/St_\mathcal{G}(n)$ of the Grigorchuk group $\mathcal{G}$. We show that Schur Multipliers of these quotients are $H_2(\math...
Necessary and sufficient conditions for the existence of limits of the form {equation*} \lim_{(x,y)\rightarrow (a,b)}\frac{f(x,y)}{g(x,y)} {equation*} are given, under the hipothesis that $f$ and $g$...
We study the Toeplitz algebra T (N ⋊ N×) and three quotients of this algebra: the C-algebra QN recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative bound...
We consider the fundamental group p of a surface of finite type equipped with the infinite generating set consisting of all simple closed curves. We show that every nilpotent quotient of p has finite ...
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of ( , )-derivation to ( , )-higher derivation and demonstrate that a filter of a...
The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple algebraic group with Lie algebra g. Fix a maximal unipotent subgroup U ⊂ G and a maximal torus T of ...

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